An algebraic rectangle - SSDD Problems - Free Printable

Final Answer:
x = 19

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Explanation:
We are given a rectangle with side lengths:
- Length = $ x + 7 $
- Width = $ x - 11 $

The perimeter of a rectangle is:
$$
\text{Perimeter} = 2 \times (\text{length} + \text{width})
$$

So plug in the expressions:
$$
2[(x + 7) + (x - 11)] = 52
$$

Simplify inside the brackets:
$$
(x + 7) + (x - 11) = 2x - 4
$$

Now multiply by 2:
$$
2(2x - 4) = 52 \\
4x - 8 = 52
$$

Add 8 to both sides:
$$
4x = 60
$$

Divide by 4:
$$
x = 15
$$

Wait — that gives x = 15, but let’s double-check. If x = 15:
- Length = 15 + 7 = 22
- Width = 15 − 11 = 4
- Perimeter = 2(22 + 4) = 2 × 26 = 52 ✔

So x = 15 is correct.

But hold on — the problem also says “Find the area of the rectangle.”
Area = length × width = $ (x+7)(x-11) $

Plug in x = 15:
$ (15+7)(15-11) = 22 × 4 = 88 $ cm²

However, the final answer requested is just x, and from perimeter alone, x = 15.

Wait — re-read the full prompt. There are *four* separate problems in the image. But the instruction says: “Solve the problem accurately” — and only one final answer is expected.

Looking again: The first problem says:
- Perimeter = 52 cm
- Write equation in terms of x
- Find value of x
- Find area

But the user’s instruction says:
→ Provide only the final correct answer.

Since the first task asks to “Find the value of x”, and that’s the most direct question, and we found x = 15, that should be the answer.

But earlier I wrote x = 19 — that was a mistake. Let me recalculate carefully:

Perimeter = 2[(x+7) + (x−11)] = 2[2x − 4] = 4x − 8
Set equal to 52:
4x − 8 = 52
4x = 60
x = 15 ✔

So correct final answer is 15.

I must correct my earlier wrong answer.

Final Answer:
15